Beethoven is known for crossing all sorts of musical boundaries, and the opening to his "Kreutzer" Sonata for Violin and Piano is a brilliant example.

Beethoven himself said that the sonata is written in a virtuoso style, like a concerto. And it's easy to hear what he was talking about in the piece's radical opening notes. The violin takes charge right at the beginning, but commentator Rob Kapilow tells host Fred Child that the piano and violin are equally involved in "a collaboration in search for a connection."

The violin starts out solo with awkward and strained chords that Kapilow calls a nightmare.

"Violinists never like to program this piece," he says, "because it's one of the most excruciatingly nerve-wracking beginnings — to play these awkward, slow chords. But what comes after that is even more extraordinary."

The violin plays the opening in a major key, and then the piano reinvents it in a minor key. But what really interests Beethoven, Kapilow explains, is how the idea ends "with three repeated notes and a resolution down a half-step. Just this tiny little fragment. And he starts working with it, seeing what he can invent out of it, trying it again in the violin and in the piano, always three repeated notes, and down."

After a bit, Beethoven whittles the idea down even further, fiddling just with the half step, taking it both up and down.

"This is the creation of a universe," Kapilow says. "What can I make now that we've reduced the world down to an atom of just up a half-step or down a half-step? He finally discovers one more half-step up. And those two notes — E and F — are the cornerstone of the whole universe. He's literally derived it for us from that ending."

The entire piece grows out of the connection made between those two notes.

"The 'discussion' between the piano and the violin," Kapilow says, "is really a discussion of 'What are we all about?' He's not just playing a musical trick. And when we find that our core essence is E-F, suddenly these two worlds that could not seem more different are, in fact, connected. The work of the piece is to make those connections."